A Revolutionary Approach In The Prediction Of Mixing Processes

Mixing processes are common in various industries like pharmaceutical, chemical or food production. An accurate prediction of the mixing process is the key to improve the efficiency and profitability, whereby conventional simulation methods like computational fluid dynamics (CFD) faces challenges in the prediction of the fluid-solid behaviour and complex kinematics as well as geometries.

Thus, this article focuses on innovative, particle-based approaches to overcome these challenges. The basics of the Smoothed Particle Hydrodynamics (SPH) and the Discrete Element Method (DEM) to capture the behaviour of the fluid and the motion of the particles, respectively, are presented.

Basics

The conventional CFD and FEM approach are based on an eulerian, mesh-based approach. For the CFD side, the navier-stokes equations, which describes the motion of viscous fluids, are solved over the faces of the finite volumes.

This method is quite accurate, well researched and industry standard in many fields. The simulation includes the meshing and discretising of the fluid volume. Therefore, the complex geometries of agitators result in difficulties during the meshing process and can negatively affect the accuracy of the simulation.

Additionally, the motion of the agitator adds another layer of complexity to the simulation. An approach to capture the motion is by remeshing every few timesteps, which will significantly increase the computational time. Another possibility is to split the mesh into a stationary and a moving part respectively for the tank and the agitator area, where an interpolation is carried out over the connecting faces.

This interpolation will lead to additional numerical errors and a slightly increased computational time. A better approach to capture the motion is to introduce moving reference frames, where for most stationary mixing process a single reference frame is suitable. With multiple moving parts or interlocking components, the CFD approach cannot cope without significantly increasing computational time and cost.

Particle-based, langrangian approaches overcome those disadvantages of the traditional methods. SPH is mesh-free and is used to simulate continuum media such as fluids, which is described as a collection of particles.

Each SPH-particle has an assigned value for properties like mass, velocity, pressure and temperature. The governing equations are also the navier-stokes equations, whereas the interaction with other SPH-particles is captured with a kernel function and the distance between the fluid particles.  

Due to discretising the fluid as particles, the SPH approach is suited for free-surface flows and problems involving complex motions and geometries. Even engaging geometries in a gearbox or a mixer with double agitators can be simulated without an increase in computational time and cost. For that reason, the SPH method is an interesting alternative to conventional methods like classical CFD.

On the other hand, the DEM, which is also a particle-based, langrangian approach, solves the equations of motion, translation and rotation, for solid particles. The interaction of solid particles is accurately captured with additional models based on physical equations like the Hertz Contact model. With the DEM, the simulation of granular flows, mixing of solids and general bulk behaviour is possible.

In mixing, the process often requires multiple materials including fluids and solids. Therefore, the prediction of fluid-solid interactions during the mixing process can be captured by a combination of the described approaches.

The CFD-DEM method for mixing should be simulated using a two-way coupled approach, where the interaction from the fluid on the solid and from the solid on the fluid is captured accurately. This approach is computationally intensive due to the blocking of fluid cells or the remeshing every time-step of the CFD simulation.

However, the SPH-DEM approach is natively two-way coupled, which captures the interactions between the fluid and solids accurately while conserving computational effort and time. Consequently, the SPH-DEM method is the most suitable approach for the prediction of fluid-solid mixing processes.

Application examples

The following application examples are intended to give an overview of simulation capabilities, whereby every kind of kinematic as well as ratio between fluid and solid fraction can be modelled. The first example shows a fully dry mixing process of a generic, laboratory size mixer, depicting different post-processing possibilities.

Figure 1: Dry mixing process

In the simulation different particle geometries, derived from real material, are implemented, whereby each group is coloured respectively. Particle sizes range from 1 to 5 mm, with an overall particle count of approximately 7 million. In general, it can be stated that the red particles are the smallest and the green are the biggest, with a particle size distribution defined for each particle group.

By making the chamber transparent the distribution of each fraction can be observed over time, from the outside as well as from the inside by using cutting planes. To get a better understanding of the process behaviour every bulk material fraction can be displayed separately.

Together with quantitative evaluations like local mixing coefficients or needed motor torque, it is possible to generate in-depth knowledge of the system and derive optimisations regarding the design or the process parameters.

The described combination of the SPH-DEM approach can be applied e.g. in dispersion problems like fluid-solid mixing, which is visualised in figure 2. The agitator in the left illustration, which rotates along its axis and additionally following a circular path, mixes 6 l of fluid and 500 g of powder. In this use case, it can be clearly observed how the powder behaves in the fluid while mixing.

It is clear to see, that due to the mixing kinematic and geometries a sufficient distribution in the fluid cannot be reached. A significant fraction of the bulk material stays contiguous at the lower chamber area and gets pulled by the agitator.

By looking at this, obviously insufficient process setup, the benefits of simulation approaches can be clearly understood, especially of you work on new agitator designs and/or must deal with completely new material combinations.

In the right figure, two agitators are mixing 2000 l of fluid, represented by 16 million SPH-elements, and 25 g of powder particles, which is represented by 10 000 particles. The aim in this simulation case was do de-mix the dispersion to generate agglomerates of the distributed particles in the fluid.

By using experimental approaches, a straightforward definition of the process in this case is time-consuming due to the not observable particles in the fluid.

Tests need to be carried out based on experience of the individual worker. By simulating this case, it is possible to track every single particle and derive the overall movement behaviour in the chamber.

Together with this and optimisations of the agitator design and adaption of process parameters, it is much easier, faster and cheaper to define the process setup by simulation. All simulations shown, can be carried out within several hours, or if high mixing times should be investigated, within a day or two.

Figure 2: Coupled SPH-DEM simulation of dispersion

One problem in processing is the mixing of fluids with comparatively high density gradients. The application example in figure 3 shows a common mixing in chemical industry. Two fluids with a density of ~780 kg/m³ and ~1300 kg/m³, respectively, are mixed using a propeller style impeller with kidney shaped blades. This mixer generates a combination of axial and radial flow, ideally for density gradients like this.

With the simulation an accurate prediction of the mixing ratio, mixing time and needed power of the drive for a series of multiple impeller speeds can be carried out.

Figure 3: Mixing of multiple phases

Conclusion

As shown above, the combination of highly innovative simulation methods like the SPH and DEM offer the possibility to analyse and optimise mixing processes of every kind in short time, with high information density and without the need for manufacturing physical machine parts.

Moreover, due to the possibility of extensive digital testing by simulating the mixing system, time- and cost-intensive machine and process adaption at the production site can be prevented.

Especially in powder mixing processes, high amounts of particles are existent which still lead to high computing times, but with constantly improving simulation code as well as increased computing power in the field of graphic cards, even these demanding processes can be simulated with a manageable number of valid simplifications.

By using simulation methods like the SPH and DEM it is possible to not only observe the mixing process itself, but also derive fundamental data for the machine design, like necessary power for the correct choice of electric engines or the loads on the machine parts.

Altogether, the digital design, optimisation and testing of agitators come along with significant benefits in the technical and economical perspective.